InterviewSolution
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InterviewSolution
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For `3xx3`matrices `Ma n dN ,`which of the following statement (s) is (are) NOT correct ?`N^T M N`is symmetricor skew-symmetric,according as `m`is symmetric or skew-symmetric.`M N-N M`is skew-symmetric for allsymmetric matrices `Ma n dNdot``M N`is symmetric for all symmetricmatrices `M a n dN``(a d jM)(a d jN)=a d j(M N)`for all invertible matrices `Ma n dNdot`A. `N^(T)MN` is symmetric or skew-symmetric, according as M is symmetric or skew-symmetricB. `MN-NM` is skew0symmetric for all symmetric matrices M and NC. MN is symmetric for all symmetric matrices M and ND. (adj M ) (adj N) = adj (MN) for all inveriblr matrices M and N. |
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Answer» Correct Answer - C::D (1) `(N^(T)MN)^(T)=N^(T)M^(T)N=N^(T)MN` if `M` is symmetric and is `-N^(T)MN` if `M` is skew symmetric (2) `(MN-NM)^(T)=N^(T) M^(T)-M^(T)N^(T)=NM-MN=-(MN-NM)`. So, `(MN-NM)` is skew symmetric (3) `(MN)^(T)=N^(T)M^(T)=NM ne MN` if `M` and `N` are symmetric. So, MN is not symmetric (4) (adj. M) (adj. N) = adj `(NM) ne` adj `(MN)` |
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